Home > Calculus > Determining Points of Inflection for a Function

What are the points of inflection of #f(x)= x^3 + 5x^2 + 4x - 3#?

Answer 1

Charles Arocha

There is only one point of inflection at #(-1.667,-0.407)#

To determine points of inflexion, we look when #f''(x)=0#

#f(x)=x^3+5x^2+4x-3#

#f'(x)=3x^2+10x+4#

#f''(x)=6x+10#

#f''(x)=0 =>6x+10=0# #x=-10/3/6=-5/3=-1.667#

#f(-5/3)=(-1.667)^3+5(-1.667)^2+4(-1.667)-3=-0.407#

graph{[-10.915, 9.08, -5.74, 4.26]} x^3+5x^2+4x-3

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Answer 2

Emily Ammerman

To find the points of inflection, you need to find the second derivative of the function, set it equal to zero, and solve for x. Then, determine the concavity of the function around those points by checking the sign of the second derivative. If the concavity changes from concave up to concave down or vice versa, those points are points of inflection.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.